**Circular Motion**

Circular motion is when a force is applied to an object perpendicular to travel creating a circular motion path

In circular motion there is:

- The
**mass**'m' - The 'r' the
**radius**(from the centre of circle) - The
**centripetal force**'F' pulling the mass towards the centre of the circle, perpendicular to the direction of travel - The
**centripetal acceleration**'a' of the mass once the centripetal force is applied i the acceleration towards the centre of the circle - The
**instantaneous velocity**'v', which is the speed of the mass once the centripetal force is removed - The
**periodic time**'T', the time for one oscillation

## Working out Instantaneous Speed

The instantaneous speed is the speed (not velocity) of the mass if no centripetal force was applied

## Working out Centripetal Acceleration

To understand centripetal acceleration - think about the forces being applied

If an object is traveling in a straight line then there is no force being applied perpendicular to travel.

Once a centripetal force is applied, using F = ma, there must be acceleration

This means the object is in constant acceleration towards the centre of the circle

To work this out the equation below is applied

If an object is traveling in a straight line then there is no force being applied perpendicular to travel.

Once a centripetal force is applied, using F = ma, there must be acceleration

This means the object is in constant acceleration towards the centre of the circle

To work this out the equation below is applied

## Working out Centripetal Force

By inserting acceleration into F = ma we get:

**Note: Centrifugal force is the opposition force to the centripetal force. It is the inertia of the object****When working out questions for the centripetal force, if the radius is constant then the centrifugal force must equal the centripetal force.**

**The centrifugal force of an object is its weight (mg)**

**Radians**

**Conical Pendulums**

Conical pendulums are masses traveling in circular motion whilst hanging from a point placed vertically above

Only two forces acting on the mass. Weight and tension in the string

The reason the mass travels in a circular shape is because of the

This means

**tension**in the string is applying enough**force vertically**to**equal the weight**and create a**centripetal force**.This means

**Tcosθ = mg**(because there is no acceleration vertically)**Tsinθ = centripetal force**